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Simplifying (7a + -2x)(x + a) = 0 Reorder the terms: (7a + -2x)(a + x) = 0 Multiply (7a + -2x) * (a + x) (7a * (a + x) + -2x * (a + x)) = 0 ((a * 7a + x * 7a) + -2x * (a + x)) = 0 Reorder the terms: ((7ax + 7a2) + -2x * (a + x)) = 0 ((7ax + 7a2) + -2x * (a + x)) = 0 (7ax + 7a2 + (a * -2x + x * -2x)) = 0 (7ax + 7a2 + (-2ax + -2x2)) = 0 Reorder the terms: (7ax + -2ax + 7a2 + -2x2) = 0 Combine like terms: 7ax + -2ax = 5ax (5ax + 7a2 + -2x2) = 0 Solving 5ax + 7a2 + -2x2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -2x)(a + x) = 0Subproblem 1
Set the factor '(7a + -2x)' equal to zero and attempt to solve: Simplifying 7a + -2x = 0 Solving 7a + -2x = 0 Move all terms containing a to the left, all other terms to the right. Add '2x' to each side of the equation. 7a + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 7a + 0 = 0 + 2x 7a = 0 + 2x Remove the zero: 7a = 2x Divide each side by '7'. a = 0.2857142857x Simplifying a = 0.2857142857xSubproblem 2
Set the factor '(a + x)' equal to zero and attempt to solve: Simplifying a + x = 0 Solving a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 a + 0 = 0 + -1x a = 0 + -1x Remove the zero: a = -1x Simplifying a = -1xSolution
a = {0.2857142857x, -1x}
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